and drive \(z\)  to 0 by iteratively updating the Lagrange multipliers \(\beta \) , where each so-called outer loop iteration uses another inner-level iterative ADMM scheme that minimizes (REF ) subject to the constraints of (REF ).
An alternative two-level decomposition for (possibly nonlinear) coupling constraints is proposed in [1]} but it depends intimately on randomized block updating of the augmented Lagrangian function which in turn requires locally tight upper bounds of the objective function with respect to each variable block, while fixing the other blocks.
